[tex]\bf a^{\frac{{ n}}{{ m}}} \implies \sqrt[{ m}]{a^{ n}} \qquad \qquad
\sqrt[{ m}]{a^{ n}}\implies a^{\frac{{ n}}{{ m}}}\\\\
-----------------------------\\\\
(x^2+78x)^{\frac{1}{5}}=3\implies \sqrt[5]{(x^2+78x)}=3
\\\\\\
\textit{now, let's raise both sides by 5}
\\\\\\\
[\sqrt[5]{(x^2+78x)}]^5=3^5\implies x^2+78x=243\implies x^2+78x-243=0
\\\\\\
\begin{array}{lcclll}
x^2&+78x&-243=0\\
&\uparrow &\uparrow \\
&81-3&81\cdot -3
\end{array}\implies (x+81)(x-3)=0[/tex]
surely, you'd know what "x" is from there
